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Cheetham, Alan H., and Douglas M. Lorenz. A Vector Approach to Size and Shape Comparisons among Zooids in Cheilostome Bryozoans. Smithsonian Contributions to Paleobiology, number 29, 55 pages, 37 figures, 19 tables, 1976.— Although zooid size and shape have long been used in comparative studies of cheilostome bryozoans, procedures for measuring these properties have been little investigated. Predominantly intussusceptive growth of buds suggests a method of comparing zooid outlines based on (1) correspondence of principal growth direction (proximal-distal axis) and (2) size and shape properties expressing differential growth about this axis. Vector properties of a wide variety of autozooidal outlines (in frontal view) were studied by principal components. Size (area within the outline) accounts for more than one-third of the variation and tends to vary less within colonies than shape, even in severely disturbed budding patterns. The portion of shape independent of size is divisible into three components. Each of the first two components accounts for about one-fourth of the total variation, the third for less than five percent. One shape component is associated with asymmetry of outline, as measured both by departure of the mean vector direction from the proximal-distal axis and by inequality of vector lengths on either side of the axis. The amount of asymmetry is small, can be either antisymmetry or fluctuating asymmetry, and varies greatly within colonies apparently with microenvironmental effects on budding patterns. The second shape component is associated with elongation (concentration of vector lengths near the mean growth direction) and distal inflation (proportion of area distal to the midpoint of the proximaldistal axis). These two variables seem less affected by microenvironment than is asymmetry. The third component accounts for only the small part of variation in elongation and distal inflation that is not positively correlated. Variation in this component suggests that distal inflation is slightly more sensitive to microenvironment than is elongation. Estimates of intrapopulation variation in one fossil species suggest that size and that part of elongation varying in opposition to distal inflation are sufficiently consistent within single populations, under the same conditions of ontogeny, astogeny, and polymorphism, to form a basis for taxonomic discrimination. Within the range of colony means for each of these two properties among the variety of outlines examined, at least three and possibly four potentially taxonomically distinct intervals can be recognized. T h e number of measurements per colony needed to detect differences between these intervals is surprisingly small. OFFICIAL PUBLICATION DATE is handstamped in a limited number of initial copies and is recorded in the Institution's annual report, Smithsonian Year. SI PRESS NUMBER 6134. SERIES COVER DESIGN: The trilobite Phacops rana Green. Library of Congress Cataloging in Publication Data Cheetham, Alan H. A vector approach to size and shape comparisons among zooids in cheilostome bryozoans. (Smithsonian contributions to paleobiology ; no. 29) Bibliography: p. Supt. of Docs, no.: SI 1.30:29 1. Cheilostomata, Fossil. 2. Invertebrate populations. 3. Vector analysis. I. Lorenz, Douglas M., joint author. II. Title. III. Series: Smithsonian Institution. Smithsonian contributions to paleobiology ; no. 29. QE70I.S56 no. 29 [QE799.C5] 560'8s 75-31747 [564'.7]